{"schema":"vela.problem-packet.v0.1","problem":770,"statement":"Let $h(n)$ be minimal such that $2^n-1,3^n-1,\\ldots,h(n)^n-1$ are mutually coprime. Does, for every prime $p$, the density $\\delta_p$ of integers with $h(n)=p$ exist? Does $\\liminf h(n)=\\infty$? Is it true that if $p$ is the greatest prime such that $p-1\\mid n$ and $p>n^\\epsilon$ then $h(n)=p$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A263647","name":"Numbers k such that 2^k-1 and 3^k-1 are coprime.","terms":"1,2,3,5,7,9,13,14,15,17,19,21,25,26,27,29,31,34,37,38,39,41,45,47,49,51,53,57,59,61,62,63,65,67,71,73,74,79,81,85,87,89,","url":"https://oeis.org/A263647"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}